. Angewandte Communications

Solvatochromism

International Edition: DOI: 10.1002/anie.201502157 German Edition: DOI: 10.1002/ange.201502157

Two-Photon Voltmeter for Measuring a Molecular Electric Field** Aleksander Rebane,* Geoffrey Wicks, Mikhail Drobizhev, Thomas Cooper, Aleksander Trummal, and Merle Uudsemaa Abstract: We present a new approach for determining the strength of the dipolar solute-induced reaction field, along with the ground- and excited-state electrostatic dipole moments and polarizability of a solvated chromophore, using exclusively one-photon and two-photon absorption measurements. We verify the approach on two benchmark chromophores N,Ndimethyl-6-propionyl-2-naphthylamine (prodan) and coumarin 153 (C153) in a series of toluene/dimethyl sulfoxide (DMSO) mixtures and find that the experimental values show good quantitative agreement with literature and our quantumchemical calculations. Our results indicate that the reaction field varies in a surprisingly broad range, 0–107 V cm¢1, and that at close proximity, on the order of the chromophore radius, the effective dielectric constant of the solute–solvent system displays a unique functional dependence on the bulk dielectric constant, offering new insight into the close-range molecular interaction.

The electronic properties of polar chromophores in solution are dominated by their interactions with the solvent environment. Understanding how the molecular electric dipole moment and polarizability behave in the ground and excited states is critical for optimizing solvent-dependent properties of materials, including absorption and fluorescence spectra as well as photo-initiated charge separation.[1] Furthermore, if the molecular dipoles and polarizabilities in the ground- and excited states could be accurately determined, then spectros[*] Dr. A. Rebane, G. Wicks, Dr. M. Drobizhev Deptartment of Physics, Montana State University 264 EPS, Bozeman, MT 59717 (USA) E-mail: [email protected] Dr. A. Rebane, A. Trummal, Dr. M. Uudsemaa National Institute of Chemical Physics and Biophysics Tallinn (Estonia) Dr. T. Cooper Air Force Research Lab Wright Patterson Air Force Base, Dayton, OH (USA) Dr. M. Uudsemaa Tallinn Institute of Technology, Tallinn (Estonia) [**] We thank Dr. Patrick Callis for discussion and Dr. Jury Stepanenko and Jake Lindquist for technical assistance. This work was supported by NIH (grant number GM098083) and Estonian Ministry of Education and research grants IUT23-9, IUT23-7, and ETF9477. Supporting information for this article is available on the WWW under http://dx.doi.org/10.1002/anie.201502157. Ó 2015 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA. This is an open access article under the terms of the Creative Commons Attribution Non-Commercial NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

7582

copy would directly probe the intrinsic electric fields acting on the chromophore,[2] thus providing important quantitative insight into solvation, catalysis, and other phenomena. Among available experimental methods, standard solvatochromism relies on several assumptions, which are typically valid only for a limited range of rigid systems.[1] Electrochromism and microwave conductivity measurements require strong external electric fields and suffer from reduced fidelity in heterogeneous environments.[3] Spectral hole-burning Stark spectroscopy[2c] offers higher selectivity and fidelity, but requires cooling of the samples to cryogenic temperatures to achieve narrow homogeneous line shapes, thus limiting its versatility, especially regarding biological systems. The vibrational Stark effect and vibrational absorption spectroscopy has been used to probe local electric fields, provided that the vibrational frequency shifts are calibrated with respect to external fields.[4] In addition, currently available techniques suffer from ambiguity regarding the boundary separating the core chromophore from its immediate surrounding solvent thus complicating distinction between the intrinsic electric field versus the externally applied voltage.[2a] Here we report an all-optical method that determines the strength of the dielectric reaction field (Ereac), the vacuum molecular electric dipole moment (mvac) and polarizability (a) in both the ground- (S0) and lowest excited (S1) singlet states, and provides quantitative estimate of the effective molecular size (a0) for two benchmark polar chromophores, prodan and C153. Our approach combines solvatochromic one-photon absorption (1PA) and femtosecond two-photon absorption (2PA) experiments, where the latter serves as a versatile alternative to the Stark effect and related techniques.[5] Details of the spectroscopic procedures, spectral data analysis, and computational methods are given in the Supporting Information. Figure 1 shows the 1PA and 2PA spectra of prodan (left) and C153 (right) in three representative mixtures of toluene and DMSO. Both prodan and C153 show a systematic red-shift and broadening of the absorption band with increasing e. Gaussian decomposition of the 1PA spectrum yields the dependence of the peak frequency and the bandwidth of the lowest energy component (dasheddotted line) on e. By extrapolating these dependencies to e = 1 we determined the vacuum peak transition frequency (nvac) and the effective “vacuum” spectral bandwidth (Dnvac ; Table 1). Here and in the following, we refer to spectral parameters or band shape of the lowest-energy transition band only. A two-level model has been shown to provide quantitative description of 2PA in the lowest-energy (0-0) component of S0 !S1 transition of polar chromophores (see the Supporting Information for details), where the 2PA cross section,

Ó 2015 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

Angew. Chem. Int. Ed. 2015, 54, 7582 –7586

Angewandte

Chemie

Figure 1. 1PA spectrum (blue line) and 2PA spectrum (pink symbols) in prodan (left) and C153 (right), each in three representative toluene:DMSO mixtures. Gaussian fit to the lowest energy band of the S0 !S1 transition (dash-dotted line); measured Dm dependence (black symbols, inserted vertical scale); predicted Dm dependence (thick dotted line). Table 1: Comparison of experimental, calculated, and literature parameter values. Literature computational values are given in italics. Prodan

C153

parameter nvac [cm¢1] Dnvac [cm¢1] a(S0) [ç3]

exp. 26 860 œ 200 1190 œ 15 27 œ 3

calc. 31 759[a]

lit.

29.8[b]

27.5[9]

Da [ç3]

46.8 œ 4.7

mvac (S0) [D]

5.8 œ 0.6

36.4[a] (vacuum) 40.2[a] (Toluene) 6.13[a]

Dmvac [D]

12.8 œ 0.6

4.2[a] (vacuum) 6.0[a] (Toluene)

a0 [ç]

6.5 œ 0.7

6.3[b]

Da [ç] p

1.8 0.65

exp. 23 505 œ 200 440 œ 10 27 œ 3 ¢6.6 œ 0.7

calc. 29 344[a]

lit.

29.9[b] 30.7[c] 5.0[a]

29.7[9]

5.2[3a]

6.7 œ 0.7

4.4–5.0[3a] 8[13] 12.73[3b]

9.4 œ 0.5

7.21[b] 7.27[c] 5.4[a]

4.7 œ 0.5

4.9[b]

0.08 0.8

5.3 œ 14[10] 4.4[11] 6.55[12] 6.97[11] 4.9[14] 6.0–9.5[10, 15] 4.88[11] 7.9[16] 4.41[11] 4.6[17]

[a] CAM-B3LYP/6-311 + + G(d,p)//B3LYP/6-311G(d,p).[8] [b] B3LYP/6-311G(d,p)//B3LYP/6-311G(d,p).[8] [c] CAM-B3LYP/6-311 + + G(d,p)//CAMB3LYP/6-311G + + (d,p)[8] (see the Supporting Information). 

s2PA(2l), is related to the permanent dipole moment change, Dm = m(S1)¢m(S0) (in Debye)[6] given in Equation (1), Angew. Chem. Int. Ed. 2015, 54, 7582 –7586

Dm ¼ 4:55   103

3 n2 þ 2

Œsffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ns2PA ð2lÞ leM ðlÞ

Ó 2015 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

ð1Þ

www.angewandte.org

7583

. Angewandte Communications where n is the solvent index of refraction, l is the transition wavelength (nm), eM is the molar extinction coefficient (m ¢1 cm¢1), and s2PA is the 2PA cross section, expressed in Gçppert–Mayer units (1 GM = 10¢50 cm4 photon¢1 s¢1). We assume here and in the following that all vector and tensor quantities are aligned with their predominant component pointing along the same coordinate axis. The black symbols in Figure 1 (Dmexp) show the value of Dm calculated from Equation (1) (inserted vertical axis). In the case of prodan, Dm shows up to a 15 % increase with increasing wavelength, whereas in C153 the value remains approximately constant. The solute static dipole polarizes the surrounding dielectric (solvent), which in turn creates a reaction electric field that shifts the energy levels of the chromophore via Stark effect, which then relates to the observed transition frequency change as given in Equations (2) and (3), n ¼ nvac ¢

Dmvac Da 2 E ¢ E hc reac 2hc reac

Dm ¼ Dmvac þ DaEreac

ð2Þ

ð3Þ

where h is PlanckÏs constant, c is the velocity of light in vacuum, Dmvac is the vacuum dipole moment change, Da = a(S1)¢a(S0) is the change of polarizability, and Ereac is the solvent field created by m(S0). Figure 2 shows the experimental correlation between the peak transition frequency and the average Dm. Fitting with Equations (2) and (3) gives the values of Dmvac and Da (Table 1).

Ereac ¼

f mvac ðS0 Þ a3 ¢ f aðS0 Þ

ð4Þ

where f represents the dependence on the dielectric constants outside and inside the volume. To account for unknown closerange solute–solvent interaction, while still complying with MaxwellÏs equations, this function may be written in the form of Equation (5) f ¼

2ðe ¢ ep Þ 2e þ ep

ð5Þ

and where the power dependence (0 ‹ p ‹ 1) ensures that the direction of the reaction field energetically stabilizes the system while satisfying the vacuum limit [Eq. (6)]. lim Ereac ¼ 0

ð6Þ

e!1

According to Equations (2) and (4), the transition frequency varies as given in Equation (7). n ¼ nvac ¢

 Œ  Œ Dmvac f mvac ðS0 Þ Da f mvac ðS0 Þ 2 ¢ hc 2hc a3 ¢ f aðS0 Þ a3 ¢ f aðS0 Þ

ð7Þ

Solvated chromophores experience heterogeneous and fluctuating solvent environments. We can quantify the local environments by a distribution of effective cavity size, P(a), which is related to the distribution of transition frequencies, P(n), as shown in Equation (8). PðaÞ ¼

3f m3vac ðS0 Þ hcða3 þ f aðS0 ÞÞ

! 1þ 2

Œ f Da PðnÞ a3 þ f aðS0 Þ

ð8Þ

The transition frequencies are assumed to follow a Gaussian distribution [see Eq. (9)], PðnÞ ¼ e¢ð Dn Þ

n¢n0 2

ð9Þ

where n0 and Dn are the center frequency and the half-width of the transition band, respectively. Combining Equations (7)–(9), and defining E0 = Ereac(a0) and ED = Ereac(a0 + Da) as the reaction field values that correspond to the peak (n0) and half-width (n0 + Dn) of the distribution, respectively, we arrive at the distribution of the cavity size a [Eq. (10)], ! Œ f Da 1þ 3 2 3 a þ f aðS0 Þ hcða þ f aðS0 ÞÞ 2  ¦Ž2 3 Dmvac Da ¨ 2 2 ð E ¢ E Þ þ E ¢ E 0 reac hc 2hc 0 reac 6 7 ¨ 2 ¦ ¡ exp4¢ 5 DnStark þ Dn2vac

PðaÞ¼ Figure 2. Dependence of Dm in prodan (empty squares) and C135 (full squares) on nvac¢n0. Extrapolation of the fits to nvac yields the vacuum dipole moment changes, Dmvac = 12.8 œ 0.6 D for prodan (dashed line) and Dmvac = 9.4 œ 0.5 D for C153 (solid line). The slopes of the fits then give the values for change in polarizability, Da = 46.8 œ 4.7 ç3 (prodan) and Da = ¢6.6 œ 0.7 ç3 (C153).

In order to obtain the vacuum ground-state dipole moment, mvac(S0), and the ground-state polarizability, a(S0), we invoked a simple phenomenological model that treats the chromophore as a polarizable point dipole embedded in a dielectric continuum in the center of a spherical volume of radius a. The strength of the reaction field acting on the dipole is given as Equation (4):[7]

7584

www.angewandte.org

3f m3vac ðS0 Þ

ð10Þ

where DnStark is defined by Equation (11). DnStark ¼

¦ Dmvac Da ¨ 2 E ¢ E2reac ðE0 ¢ Ereac Þ þ 2hc 0 hc

ð11Þ

Inserting our experimental values Dmvac, Da, nvac, and Dnvac into the model and performing global fitting of the calculated 1PA profiles to the experimental shapes (see the Supporting Information for details), we obtain the remaining parameters,

Ó 2015 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

Angew. Chem. Int. Ed. 2015, 54, 7582 –7586

Angewandte

Chemie

mvac(S0), a(S0), a0, Da, and p (Table 1). The experimental ground-state values mvac(S0) and a(S0) agree quantitatively with the corresponding calculated values and the literature data, both for prodan and C153. The experimental Dmvac = 12.8 œ 0.6 D for prodan and Dmvac = 9.4 œ 0.5 D for C153 agree well with previous measurements, however, are about a factor of two above our calculated values. In prodan the experimental polarizability change, Da, agrees very well with the calculated value, whereas in C153 the value is much smaller, making it effectively close to zero. Despite the fact that we made no a priori assumptions about the size of the molecule, our estimated average cavity size, a0, agrees surprisingly well with the calculated molecular dimensions. For prodan, we calculated a molecular radius of 6.3 è,[8] which compares well to our experimental value, a0 = 6.5 œ 0.7 è. Similarly, for C153 we calculated the effective radius in the direction F¢C···N¢ C¢H to be 4.9 è, which is also very close to our experimental value, a0 = 4.7 œ 0.5 è. As a further independent check, we used Equations (2) and (3) to predict how Dm changes as a function of n within the absorption band (thick dotted line in Figure 1). The results are in good agreement with the measured dependence, and demonstrate that Dm is not necessarily constant, but may vary within the band. Figure 3 shows the distribution of Ereac, which appears to vary in a broad range, 0–107 V cm¢1, essentially caused by diverse local environments. Fluctuations of dielectric environment were previously used to explain temporal fluctuations of the fluorescence lifetime in single molecules.[18] Both prodan and C153 show increase of average Ereac with increasing e, with the respective maximum values, Ereac … 5.0 × 106 and 1.0 × 107 V cm¢1. The larger reaction field in C153 is due to the larger ground-state dipole moment as well as because of smaller a0. Also, C153 lacks the flexibility of prodanÏs propyl- and dimethylamino groups, which is reflected in its smaller Da and narrower Ereac distribution. Finally, by equating f to the well-known expression for the field enhancement factor in spherical volume [Eq. (12)],

we find functional form for the effective interior dielectric constant ein [Eq. (13)], Š ein ¼

Œ2 Œ ‰1=2  1 2e 1 þe þ ¢ þe f f f

ð13Þ

which may be viewed as dielectric continuum approximation of the solute–solvent system at close proximity, on the order of the chromophore radius. Figure 4 plots the resulting

Figure 4. Functional dependence of ein from Equation (13) for experimental values of p.

dependence of ein on e for the experimental values of p obtained for prodan (filled symbols) and C153 (open symbols). The range of bulk dielectric constant values used in our measurements, e = 2.38–47.6, lies between the dashed vertical lines, whereas the corresponding “internal” dielectric constant, ein = 1.5–2.4 agrees well with the commonly assumed value, ein = nsolute2 … 2.[2a, 7] We conclude that this new all-optical method provides an improved quantitative estimation of the average strength and distribution of the dielectric reaction field acting on a dipolar chromophore in different solvents, along with the values of  Œ Œ solute dipole moment and polarizability in the ground- and p 2ðe ¢ e Þ 1 2ðe ¢ ein Þ ð12Þ ¼ f ¼ excited electronic states, including the effective molecular p em 2e þ e 2e þ ein radius. The technique is applicable at ambient temperatures, and does not rely on fluorescence emission or externally applied fields, making it a versatile alternative to standard techniques. A simple phenomenological model based on the continuum dielectric solution of MaxwellÏs equations is in good quantitative agreement with experimental observations. Finally, our results indicate that the effective Figure 3. Probability density of the reaction field for different e for a) prodan and b) C153.

Angew. Chem. Int. Ed. 2015, 54, 7582 –7586

Ó 2015 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

www.angewandte.org

7585

. Angewandte Communications dielectric constant near the chromophore exhibits a unique functional dependence on the bulk dielectric constant, which may yield valuable insight into local intermolecular interactions in solvated dipolar systems. Keywords: intramolecular charge transfer · molecular reaction field · solvatochromism · solvent effects · two-photon absorption spectroscopy How to cite: Angew. Chem. Int. Ed. 2015, 54, 7582 – 7586 Angew. Chem. 2015, 127, 7692 – 7696 [1] J. R. Lakowicz, Principles of Fluorescence Spectroscopy, 3rd ed., Springer, New York, NY, 2006, and references therein. [2] a) S. D. Fried, L. P. Wang, S. G. Boxer, P. Ren, V. S. Pande, J. Phys. Chem. B 2013, 117, 16236 – 16248; b) L. Onsager, J. Am. Chem. Soc. 1936, 58, 1486 – 1493; c) E. Vauthey, K. Holliday, C. Wei, A. Renn, U. P. Wild, Chem. Phys. 1993, 171, 253 – 263; d) I. Renge, Chem. Phys. 1992, 167, 173 – 184. [3] a) A. Samanta, R. W. Fessenden, J. Phys. Chem. A 2000, 104, 8972 – 8975; b) N. A. Nemkovich, W. Baumann, J. Photochem. Photobiol. A 2007, 185, 26 – 31. [4] a) M. Saggu, N. M. Levinson, S. G. Boxer, J. Am. Chem. Soc. 2011, 133, 17414 – 17419; b) E. S. Park, S. S. Andrews, R. B. Hu, S. G. Boxer, J. Phys. Chem. B 1999, 103, 9813 – 9817. [5] M. Drobizhev, N. S. Makarov, S. E. Tillo, T. E. Hughes, A. Rebane, Nat. Methods 2011, 8, 393 – 399. [6] A. Rebane, M. Drobizhev, N. S. Makarov, E. Beuerman, J. E. Haley, D. M. Krein, A. R. Burke, J. L. Flikkema, T. M. Cooper, J. Phys. Chem. A 2011, 115, 4255 – 4262. [7] B. S. Brunschwig, S. Ehrenson, N. Sutin, J. Phys. Chem. 1987, 91, 4714 – 4723. [8] Gaussian 09, Revision B.01, 2009, M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov,

7586

www.angewandte.org

[9] [10] [11] [12] [13] [14] [15]

[16] [17] [18]

J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, ©. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski, D. J. Fox, Gaussian, Gaussian, Inc., Wallingford, CT.. R. Bosque, J. Sales, J. Chem. Inf. Comput. Sci. 2002, 42, 1154 – 1163. W. Baumann, Z. Nagy, Pure Appl. Chem. 1993, 65, 1729 – 1732. A. Chowdhury, S. A. Locknar, L. L. Premvardhan, L. A. Peteanu, J. Phys. Chem. A 1999, 103, 9614 – 9625. C. R. Moylan, J. Phys. Chem. 1994, 98, 13513 – 13516. A. Balter, W. Nowak, W. Pawelkiewicz, A. Kowalczyk, Chem. Phys. Lett. 1988, 143, 565 – 570. A. Samanta, R. W. Fessenden, J. Phys. Chem. A 2000, 104, 8577 – 8582. a) M. L. Horng, J. A. Gardecki, A. Papazyan, M. Maroncelli, J. Phys. Chem. 1995, 99, 17311 – 17337; b) S. N. Smirnov, C. L. Braun, Rev. Sci. Instrum. 1998, 69, 2875 – 2887; c) M. Maroncelli, G. R. Fleming, J. Chem. Phys. 1987, 86, 6221 – 6239. P. V. Kumar, M. Maroncelli, J. Chem. Phys. 1995, 103, 3038 – 3060. M. Schmollngruber, C. Schroder, O. Steinhauser, Phys. Chem. Chem. Phys. 2014, 16, 10999 – 11009. R. A. L. Vallee, M. Van Der Auweraer, F. C. De Schryver, D. Beljonne, M. Orrit, ChemPhysChem 2005, 6, 81 – 91.

Received: March 6, 2015 Published online: May 8, 2015

Ó 2015 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

Angew. Chem. Int. Ed. 2015, 54, 7582 –7586

Two-photon voltmeter for measuring a molecular electric field.

We present a new approach for determining the strength of the dipolar solute-induced reaction field, along with the ground- and excited-state electros...
1MB Sizes 0 Downloads 7 Views